Statistical Efficiency of Single- and Multi-step Models for Forecasting and Control
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arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866908910440415232 |
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| author | Somalwar, Anne Lee, Bruce D. Pappas, George J. Matni, Nikolai |
| author_facet | Somalwar, Anne Lee, Bruce D. Pappas, George J. Matni, Nikolai |
| contents | Compounding error, where small prediction mistakes accumulate over time, presents a major challenge in learning-based control. A common remedy is to train multi-step predictors directly instead of rolling out single-step models. However, it is unclear when the benefits of multi-step predictors outweigh the difficulty of learning a more complex model. We provide the first quantitative analysis of this trade-off for linear dynamical systems. We study three predictor classes: (i) single step models, (ii) multi-step models, and (iii) single step models trained with multi-step losses. We show that when the model class is well-specified and accurately captures the system dynamics, single-step models achieve the lowest asymptotic prediction error. On the other hand, when the model class is misspecified due to partial observability, direct multi-step predictors can significantly reduce bias and improve accuracy. We provide theoretical and empirical evidence that these trade-offs persist when predictors are used in closed-loop control. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_23465 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Statistical Efficiency of Single- and Multi-step Models for Forecasting and Control Somalwar, Anne Lee, Bruce D. Pappas, George J. Matni, Nikolai Systems and Control Compounding error, where small prediction mistakes accumulate over time, presents a major challenge in learning-based control. A common remedy is to train multi-step predictors directly instead of rolling out single-step models. However, it is unclear when the benefits of multi-step predictors outweigh the difficulty of learning a more complex model. We provide the first quantitative analysis of this trade-off for linear dynamical systems. We study three predictor classes: (i) single step models, (ii) multi-step models, and (iii) single step models trained with multi-step losses. We show that when the model class is well-specified and accurately captures the system dynamics, single-step models achieve the lowest asymptotic prediction error. On the other hand, when the model class is misspecified due to partial observability, direct multi-step predictors can significantly reduce bias and improve accuracy. We provide theoretical and empirical evidence that these trade-offs persist when predictors are used in closed-loop control. |
| title | Statistical Efficiency of Single- and Multi-step Models for Forecasting and Control |
| topic | Systems and Control |
| url | https://arxiv.org/abs/2603.23465 |